| Abstract: |
| Minimum action methods provide a powerful framework for analyzing rare transitions in stochastic dynamical systems, but their practical performance is often limited by time truncation and parameter sensitivity in infinite-horizon problems. We propose an efficient Laguerre spectral minimum action method for computing quasi-potentials associated with fixed points of dynamical systems. Based on the large deviation framework, the method computes minimum action transition paths by formulating the problem on a semi-infinite time interval and discretizing the temporal direction using Laguerre functions. An appropriate time-scaling strategy is incorporated to enhance accuracy and convergence of the Laguerre spectral approximation. To efficiently handle nonlinear terms, we develop an improved procedure for evaluating Laguerre functions at Gauss--Radau quadrature points, which enables stable double-precision computations with a large number of Laguerre modes. Numerical analysis and experiments are presented to illustrate the accuracy and efficiency of the proposed method. |
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